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Additional file 1.

In curved environments, geometric constraints can result in cellular competition for space. Quantitative information about cell geometry was extracted to explore how columnar-like cells fit within the curved anterior of the Drosophila embryo. Cell deformations and cell rearrangements enable packing in this highly curved region., Organ and tissue formation are complex three-dimensional processes involving cell division, growth, migration, and rearrangement, all of which occur within physically constrained regions. However, analyzing such processes in three dimensions in vivo is challenging. Here, we focus on the process of cellularization in the anterior pole of the early Drosophila embryo to explore how cells compete for space under geometric constraints. Using microfluidics combined with fluorescence microscopy, we extract quantitative information on the three-dimensional epithelial cell morphology. We observed a cellular membrane rearrangement in which cells exchange neighbors along the apical-basal axis. Such apical-to-basal neighbor exchanges were observed more frequently in the anterior pole than in the embryo trunk. Furthermore, cells within the anterior pole skewed toward the trunk along their long axis relative to the embryo surface, with maximum skew on the ventral side. We constructed a vertex model for cells in a curved environment. We could reproduce the observed cellular skew in both wild-type embryos and embryos with distorted morphology. Further, such modeling showed that cell rearrangements were more likely in ellipsoidal, compared with cylindrical, geometry. Overall, we demonstrate that geometric constraints can influence three-dimensional cell morphology and packing within epithelial tissues.

The movement and deformation characteristics of an active fault zone are an important prerequisite for the stability analysis of cross-fault project sites and breaking resistance design research. Based on the global positioning system (GPS) data of the Crustal Movement Observation Network of China, a GPS velocity clustering algorithm to avoid the uncertainties of block division results from geological data is proposed and applied for velocity field analysis of Yunnan province. Using the data of active faults in the central Yunnan water diversion project area and the clustering results along with a block rotation and uniform strain model, the current slip rates of the main fault were obtained by using the difference between the speeds of the same point at the boundary of neighboring blocks. Furthermore, using the 1999–2007, 2009–2013, and 2013–2015 GPS velocity field data as the constraints, the relation between the spatial points and velocities was established based on the least squares collocation theory. The distribution of strain rates in the central Yunnan water diversion project area were resolved by the spherical strain calculation method, and the dynamic variation characteristics were analyzed using regional historical earthquakes and fault properties. The results of this study show that Xiaojinhe–Lijiang and Xiaojiang faults currently have noticeable strike–slip motion. The southern Xiaojinhe–Lijiang and Xiaojiang faults have always been two strong deformation zones, and the extensional deformations in Longpan–Qiaohou, Lijiang–Jianchuan, and Chenghai–Binchuan regions are being enhanced. Xiaojiang fault is the zone with the maximum shear strain rate. These results indicate that the deformation distribution characteristics are closely related to the characteristics of the activity features of the major faults in the region.